The numerical solution of the steady state solid fuel ignition model and its optimal control

We present a finite difference multigrid technique that efficiently solves optimal control problems associated with the steady state solid fuel ignition model. This is a nonlinear indefinite problem which gives rise to singular optimal control systems. Regarding the direct problem, necessary and sufficient conditions for existence of solutions are given and second-order convergence of numerical solution errors with respect to the mesh size is proven. A robust nonlinear multigrid method is implemented to validate this convergence estimate. Two optimal control strategies for solid fuel ignition phenomena are considered and compared. The corresponding optimality systems are solved to second-order accuracy by a multigrid method whose convergence properties are independent of the values of the weights in the cost functionals and of the number of grid points.